Find Square Roots w/o Calculator by Hand Quickly & Easily

Learn how to find approximate square roots using a simple one-step technique which can be done in your head or using a small scrap of paper and pencil in less than a minute accurate to the tenth’s place.

Error in Video: The factors of 78 are 2, 3, and 13 and the factors of 12 are 2, 3, 4, and 6. So, I was wrong about the GCF—it’s 3, not 2.

Limitations & Purpose of this Technique:

1. The accuracy of this technique diminishes as the number you want to approximate the square root of approaches a perfect square. For example, this method will more accurately approximate the square root of 42 than it would 24 or 82 since those latter two numbers are extremely close to the perfect squares 25 and 81, respectively, while 42 is about halfway between its two nearest perfect squares: 36 and 49.

2. This is a single iteration process which means there is no infinite recursion such as the Newton-Raphson method and neither does it follow a convergence pattern such as can be done using the Taylor series. However, this second limitation is more of an intentional “feature” than an intrinsic flaw—those above-referenced methods are ways by which one can, by hand, precisely approximate a square root to several decimal places of accuracy but that is not the purpose of this method. This method is intended to be, above all, *simple and quick*—I modified a more complicated recursive iterative method to this “one step” approach in order to teach 9-12 year olds how to approximate square roots. None of the above-referenced methods are appropriate for this age range and this method is easy to remember forever and can be used for quick work in a number of practical trades. If you need several decimal places of precision, I recommend using a calculator.